Why This Book Is for You
Art and science sometimes appear in juxtaposition, one aesthetic, the other analytical. This book bridges the two cultures. I have written it for the artist who is willing to devote a modicum of effort to understanding the mathematical world of the scientist and for the scientist who often overlooks the beauty that lurks just beneath even the simplest equations.
If you are neither artist nor scientist, but own a personal computer for which you would like to find an exciting new use, this book is also for you. Fractals generated by computer represent a new art form that anyone can appreciate and appropriate. You don’t have to know mathematics beyond elementary algebra, and you don’t have to be an expert programmer. This book explains a simple, new technique for generating a class of fractals called strange attractors. Unlike other books about fractals that teach you to reproduce well-known patterns, this one will let you produce your own unlimited variety of displays and musical sounds with a single program. Almost none of the patterns you produce will ever have been seen before.
To get the most out of this book, you will need a personal computer, though it need not be a fancy one. It should have a monitor capable of displaying graphics, preferably in color. Some knowledge of BASIC is useful, although you can just type in the listings even if you don’t understand them completely. For those of you who are C programmers, I have provided an appendix with an equivalent version in C. You may find the exercises in this book an enjoyable way to hone your programming skills. As you progress through the book, you will gradually develop a very sophisticated computer program. Each step is relatively simple and brings exciting new things to see and explore. Alternately, you can use the accompanying disk immediately to begin making your own collection of strange attractors.
Strange Attractors
How to find them, those regions
Of space where the equation traces
Over and over a kind of path,
Like the moth that batters its way
Back toward the light
Or, hearing the high cry of the bat,
Folds its wings in a rolling dive?
And ourselves, fluttering toward and away
In a pattern that, given enough
Dimensions and point-of-view,
Anyone living there could plainly see—
Dance and story, advance, retreat,
A human chaos that some slight
Early difference altered irretrievably?
For one, the sound of her mother
Crying. For this other,
The hands that soothed
When he was sick. For a third,
The silence that collects
Around certain facts. And this one,
Sent to bed, longing for a nightlight.
Though we think this time to escape,
Holding a head up, nothing wrong,
Finding a way to beat the system,
Talking about anything else—
Travel, the weather, time
At the flight simulator—for some
The journey circles back
To those strange, unpredictable attractors,
Secrets we can neither speak nor leave.
—Robin S. Chapman